Bernstein widths of embedding operators of Lebesgue spaces

Let $(K,\mu)$ be a measurable space, and let $\mu(K)=1$. Let
$$ \textrm I_{p,q}\colon L^p\,(K,\mu)\longrightarrow L^q(K,\mu) $$
be the embedding operator. The Bernstein widths of $\textrm I_{p,q}$ are considered.